Let's say your speakers are 10" deep or so. You say 1.5' from these to back wall. That means an AT screen in front is already at least about 2.5' from the back wall. Accounting for thickness of your noggin, let's pretend your eyeballs are 2' from back wall. (Further would likely be better for audio, btw.)
You never specified which wall was 13' (or did I miss it), but let's pretend that's length. 13 - 2.5 - 2 = 8.5' only. This means that even a very modest screen of 76" (16:9) will give you a 36 deg viewing angle. After much playing around, I prefer 42, and wouldn't change a thing myself, and if you were like me that would still be relatively modest at 90". I think poster above might be around 45 deg or so.
But let's say you get further away from the back wall to improve your audio situation. All of a sudden, the screen needs to be smaller and smaller. Anyway, I think you get my point; your need for lumens might not be as bad as it sometimes is with others who are looking for considerably larger screens.
Tools for you:
Viewing Distance Calculator
TV Calculator
Using the second tool, I could tell you that you that the PJ would only need 71% of the brightness on the 76" screen, to match what it would normally do on the 90" (which is already considered modest, btw). For example the larger 90" here would only need 67% of the brightness on what it can normally do on the 110".
I don't think you got as hosed as BMX might think you did, I think it might be a decent projector for that money, assuming it's been well cared for, with relatively low hours (which you probably don't know, lamp timer probably gets reset each time, and I agree that you are extremely unrealistic about lamp hours). It was a direct competitor to my own projector, the RS1, not quite as bright, but probably a little quiter as a result. I don't think you would call it a screaming deal either, but there might be value here IMO. Though if you had more play money, of course I'd vote for new as well, but you have to pay to play. Seeing McIntosh gear up front, I'm thinking you could probably have swung a new one if you wanted too, but whatever. Also, it's not quite 7 years old either. It was introduced at CEDIA in the fall of 2007, which means consumers in the US weren't really picking them up in earnest until 2008, which is only 4 years ago. Sort of.
Darken the room some, I think you'll be ok. Chris Seymour said "may" for a reason, but you could say that about any darn screen.
Definitely get anything with a light on it away from the front. The alternative to moving the rack would be to instead switch the couch over to the front wall, making it the new back wall, with the rack on your side. Hey the HDMI run will be shorter if the PJ is close to the rack I suppose. EVEN THEN, I highly recommend doing the following: putting each component display to minimum brightness, liberal use of window tint on these displays just don't cover IR sensors, and even the use of black tape if need be. You know, just one little tiny uncontrolled light source like a night light, candle, whatever, so dramatically decreases the PQ level, it's like the difference between a $2,000 projector, and $10,000 projector. In the case of the projector world, the room truly is the end all be all, in a way.
If you do go with a solid screen, the Carada that BMX suggests happens to be Seymour's preferred solid screen for the money, FWIW, and that says something.
Well- do you need a different screen than (insert any brand here) due to the lumens? It sure is possible, but that depends on your light control inside the room, and the size of the screen. They are equally important for your intents and purposes.
